MAYBE

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict Trs:
  { minus(s(x), y) -> if(gt(s(x), y), x, y)
  , if(true(), x, y) -> s(minus(x, y))
  , if(false(), x, y) -> 0()
  , gt(s(x), s(y)) -> gt(x, y)
  , gt(s(x), 0()) -> true()
  , gt(0(), y) -> false()
  , gcd(x, y) -> if1(ge(x, y), x, y)
  , if1(true(), x, y) -> if2(gt(y, 0()), x, y)
  , if1(false(), x, y) -> if3(gt(x, 0()), x, y)
  , ge(x, 0()) -> true()
  , ge(s(x), s(y)) -> ge(x, y)
  , ge(0(), s(x)) -> false()
  , if2(true(), x, y) -> gcd(minus(x, y), y)
  , if2(false(), x, y) -> x
  , if3(true(), x, y) -> gcd(x, minus(y, x))
  , if3(false(), x, y) -> y }
Obligation:
  runtime complexity
Answer:
  MAYBE

None of the processors succeeded.

Details of failed attempt(s):
-----------------------------
1) 'WithProblem (timeout of 60 seconds)' failed due to the
   following reason:
   
   Computation stopped due to timeout after 60.0 seconds.

2) 'Best' failed due to the following reason:
   
   None of the processors succeeded.
   
   Details of failed attempt(s):
   -----------------------------
   1) 'WithProblem (timeout of 30 seconds) (timeout of 60 seconds)'
      failed due to the following reason:
      
      Computation stopped due to timeout after 30.0 seconds.
   
   2) 'Best' failed due to the following reason:
      
      None of the processors succeeded.
      
      Details of failed attempt(s):
      -----------------------------
      1) 'bsearch-popstar (timeout of 60 seconds)' failed due to the
         following reason:
         
         The processor is inapplicable, reason:
           Processor only applicable for innermost runtime complexity analysis
      
      2) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due
         to the following reason:
         
         The processor is inapplicable, reason:
           Processor only applicable for innermost runtime complexity analysis
      
   
   3) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed
      due to the following reason:
      
      None of the processors succeeded.
      
      Details of failed attempt(s):
      -----------------------------
      1) 'Bounds with perSymbol-enrichment and initial automaton 'match''
         failed due to the following reason:
         
         match-boundness of the problem could not be verified.
      
      2) 'Bounds with minimal-enrichment and initial automaton 'match''
         failed due to the following reason:
         
         match-boundness of the problem could not be verified.
      
   

3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
   due to the following reason:
   
   We add the following weak dependency pairs:
   
   Strict DPs:
     { minus^#(s(x), y) -> c_1(if^#(gt(s(x), y), x, y))
     , if^#(true(), x, y) -> c_2(minus^#(x, y))
     , if^#(false(), x, y) -> c_3()
     , gt^#(s(x), s(y)) -> c_4(gt^#(x, y))
     , gt^#(s(x), 0()) -> c_5()
     , gt^#(0(), y) -> c_6()
     , gcd^#(x, y) -> c_7(if1^#(ge(x, y), x, y))
     , if1^#(true(), x, y) -> c_8(if2^#(gt(y, 0()), x, y))
     , if1^#(false(), x, y) -> c_9(if3^#(gt(x, 0()), x, y))
     , if2^#(true(), x, y) -> c_13(gcd^#(minus(x, y), y))
     , if2^#(false(), x, y) -> c_14(x)
     , if3^#(true(), x, y) -> c_15(gcd^#(x, minus(y, x)))
     , if3^#(false(), x, y) -> c_16(y)
     , ge^#(x, 0()) -> c_10()
     , ge^#(s(x), s(y)) -> c_11(ge^#(x, y))
     , ge^#(0(), s(x)) -> c_12() }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { minus^#(s(x), y) -> c_1(if^#(gt(s(x), y), x, y))
     , if^#(true(), x, y) -> c_2(minus^#(x, y))
     , if^#(false(), x, y) -> c_3()
     , gt^#(s(x), s(y)) -> c_4(gt^#(x, y))
     , gt^#(s(x), 0()) -> c_5()
     , gt^#(0(), y) -> c_6()
     , gcd^#(x, y) -> c_7(if1^#(ge(x, y), x, y))
     , if1^#(true(), x, y) -> c_8(if2^#(gt(y, 0()), x, y))
     , if1^#(false(), x, y) -> c_9(if3^#(gt(x, 0()), x, y))
     , if2^#(true(), x, y) -> c_13(gcd^#(minus(x, y), y))
     , if2^#(false(), x, y) -> c_14(x)
     , if3^#(true(), x, y) -> c_15(gcd^#(x, minus(y, x)))
     , if3^#(false(), x, y) -> c_16(y)
     , ge^#(x, 0()) -> c_10()
     , ge^#(s(x), s(y)) -> c_11(ge^#(x, y))
     , ge^#(0(), s(x)) -> c_12() }
   Strict Trs:
     { minus(s(x), y) -> if(gt(s(x), y), x, y)
     , if(true(), x, y) -> s(minus(x, y))
     , if(false(), x, y) -> 0()
     , gt(s(x), s(y)) -> gt(x, y)
     , gt(s(x), 0()) -> true()
     , gt(0(), y) -> false()
     , gcd(x, y) -> if1(ge(x, y), x, y)
     , if1(true(), x, y) -> if2(gt(y, 0()), x, y)
     , if1(false(), x, y) -> if3(gt(x, 0()), x, y)
     , ge(x, 0()) -> true()
     , ge(s(x), s(y)) -> ge(x, y)
     , ge(0(), s(x)) -> false()
     , if2(true(), x, y) -> gcd(minus(x, y), y)
     , if2(false(), x, y) -> x
     , if3(true(), x, y) -> gcd(x, minus(y, x))
     , if3(false(), x, y) -> y }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {3,5,6,14,16} by
   applications of Pre({3,5,6,14,16}) = {1,4,11,13,15}. Here rules are
   labeled as follows:
   
     DPs:
       { 1: minus^#(s(x), y) -> c_1(if^#(gt(s(x), y), x, y))
       , 2: if^#(true(), x, y) -> c_2(minus^#(x, y))
       , 3: if^#(false(), x, y) -> c_3()
       , 4: gt^#(s(x), s(y)) -> c_4(gt^#(x, y))
       , 5: gt^#(s(x), 0()) -> c_5()
       , 6: gt^#(0(), y) -> c_6()
       , 7: gcd^#(x, y) -> c_7(if1^#(ge(x, y), x, y))
       , 8: if1^#(true(), x, y) -> c_8(if2^#(gt(y, 0()), x, y))
       , 9: if1^#(false(), x, y) -> c_9(if3^#(gt(x, 0()), x, y))
       , 10: if2^#(true(), x, y) -> c_13(gcd^#(minus(x, y), y))
       , 11: if2^#(false(), x, y) -> c_14(x)
       , 12: if3^#(true(), x, y) -> c_15(gcd^#(x, minus(y, x)))
       , 13: if3^#(false(), x, y) -> c_16(y)
       , 14: ge^#(x, 0()) -> c_10()
       , 15: ge^#(s(x), s(y)) -> c_11(ge^#(x, y))
       , 16: ge^#(0(), s(x)) -> c_12() }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { minus^#(s(x), y) -> c_1(if^#(gt(s(x), y), x, y))
     , if^#(true(), x, y) -> c_2(minus^#(x, y))
     , gt^#(s(x), s(y)) -> c_4(gt^#(x, y))
     , gcd^#(x, y) -> c_7(if1^#(ge(x, y), x, y))
     , if1^#(true(), x, y) -> c_8(if2^#(gt(y, 0()), x, y))
     , if1^#(false(), x, y) -> c_9(if3^#(gt(x, 0()), x, y))
     , if2^#(true(), x, y) -> c_13(gcd^#(minus(x, y), y))
     , if2^#(false(), x, y) -> c_14(x)
     , if3^#(true(), x, y) -> c_15(gcd^#(x, minus(y, x)))
     , if3^#(false(), x, y) -> c_16(y)
     , ge^#(s(x), s(y)) -> c_11(ge^#(x, y)) }
   Strict Trs:
     { minus(s(x), y) -> if(gt(s(x), y), x, y)
     , if(true(), x, y) -> s(minus(x, y))
     , if(false(), x, y) -> 0()
     , gt(s(x), s(y)) -> gt(x, y)
     , gt(s(x), 0()) -> true()
     , gt(0(), y) -> false()
     , gcd(x, y) -> if1(ge(x, y), x, y)
     , if1(true(), x, y) -> if2(gt(y, 0()), x, y)
     , if1(false(), x, y) -> if3(gt(x, 0()), x, y)
     , ge(x, 0()) -> true()
     , ge(s(x), s(y)) -> ge(x, y)
     , ge(0(), s(x)) -> false()
     , if2(true(), x, y) -> gcd(minus(x, y), y)
     , if2(false(), x, y) -> x
     , if3(true(), x, y) -> gcd(x, minus(y, x))
     , if3(false(), x, y) -> y }
   Weak DPs:
     { if^#(false(), x, y) -> c_3()
     , gt^#(s(x), 0()) -> c_5()
     , gt^#(0(), y) -> c_6()
     , ge^#(x, 0()) -> c_10()
     , ge^#(0(), s(x)) -> c_12() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..